[postgis-users] bow-tie polygons and the like
Martin Davis
mbdavis at refractions.net
Tue Apr 1 15:14:46 PDT 2008
Chris,
This is a classic self-intersecting polygon, which self-touches at a
single point. These are invalid according to the OGC model. They are
valid in some other spatial models (notably ArcSDE), where they are
referred to as "inverted polygons", and are used to represent polygons
with a hole that touches an edge. In the OGC model, that situation must
be represented as a polygon with a shell ring and a separate hole ring
(which is in turn invalid in ArcSDE).
You can inter-convert between the two models, but it does require some
fussy bookkeeping.
I'm a bit surprised by the area discrepancy - even if this shape is
illegal, the area computation should be well-defined. At least, that's
the way it would work in JTS/GEOS. The area code in PostGIS may be
different, however.
Chris Hermansen wrote:
> Martin, all;
>
> Here is the wkt for the enclosing polygon:
>
> 53327 | SRID=1;POLYGON((1224673.7804 499721.97084,1224664.2479
> 499721.56584,1224639.311 499709.63254,1224658.0919
> 499675.28084,1224664.2479 499721.56584,1224673.1624
> 499747.57644,1224676.7094 499739.52814,1224676.916
> 499740.76654,1224692.459 499812.83074,1224668.6628
> 499811.81964,1224658.0339 499811.36804,1224630.597
> 499769.81704,1224627.078 499734.63704,1224622.024
> 499724.36664,1224616.0171 499712.16004,1224595.8521
> 499691.28704,1224573.8378 499685.40964,1224561.8108
> 499682.19864,1224555.2798 499681.92114,1224553.7247
> 499680.03974,1224549.0699 499678.79694,1224549.2472
> 499674.62264,1224550.0095 499656.68104,1224534.9948
> 499656.04304,1224527.759 499655.73564,1224525.1614
> 499651.95204,1224525.556 499642.66424,1224526.0666
> 499630.64754,1224527.1273 499605.67644,1224502.1236
> 499604.61414,1224503.1844 499579.64304,1224478.1807
> 499578.58064,1224479.2415 499553.60954,1224466.8676
> 499553.08384,1224458.2316 499552.71694,1224454.6943
> 499541.79814,1224454.9879 499534.88804,1224450.0691
> 499527.35404,1224431.6821 499499.19104,1224417.7948
> 499486.96474,1224416.8351 499484.88504,1224410.5131
> 499470.72264,1224410.1876 499470.02924,1224409.5706
> 499468.87504,1224408.8795 499467.76364,1224408.658
> 499467.43914,1224405.783 499463.31414,1224405.2422
> 499462.57484,1224404.4119 499461.56314,1224404.1681
> 499461.29034,1224397.5431 499454.00904,1224397.4215
> 499453.87654,1224386.8436 499442.45874,1224379.5284
> 499434.45384,1224369.2823 499422.31714,1224369.0369
> 499422.03184,1224368.1423 499421.07654,1224367.1869
> 499420.18194,1224366.6558 499419.73214,1224355.8777
> 499410.92434,1224341.2698 499396.04914,1224341.1422
> 499395.92044,1224329.9105 499384.68884,1224324.2636
> 499378.59734,1224302.9088 499332.37814,1224392.4667
> 499355.14934,1224393.122 499355.91874,1224487.2901
> 499450.78514,1224496.2156 499459.77684,1224493.9911
> 499462.52154,1224506.465 499484.35254,1224564.6899
> 499528.85044,1224605.2731 499587.61344,1224614.2741
> 499599.88254,1224625.0241 499614.53564,1224653.1386
> 499652.85784,1224658.315 499659.91354,1224667.3321
> 499683.31754,1224673.7804 499721.97084))
>
> point 0 is the se corner of the bow tie. point 1 is the "knot" of the
> bow-tie, and you will see it reappear as point 4. the triangle made up
> of points 1, 2, 3, 4 is the one I mentioned previously that goes in the
> wrong direction.
>
> I must confess to a slight simplification in my previous e-mails; the
> bow tie is not quite perfectly formed; it's southeast corner has been
> trimmed off so that the eastern "triangle" is actually a quadrilateral.
> Sorry :D
>
> Martin Davis wrote:
>
>> Chris,
>>
>> Can you post the WKT for the problematic feature? (Ascii art is
>> nifty, but not really a substitute for a 1600x1200 pixel display... 8^)
>>
>> Chris Hermansen wrote:
>>
>>> Hi Nicolas, all;
>>>
>>> Nicolas, I understand your comment. But after looking at the data some
>>> more in OpenJump, that appears to not be my problem.
>>>
>>> If I load the PostGIS theme into OpenJump and run the QA on it, I see
>>> that it is the polygon that contains the bow-tie shaped figure that is
>>> the problem.
>>>
>>> I can represent this schematically as:
>>>
>>> +-----------------+
>>> | |
>>> | |><|
>>> | |
>>> +-----------------+
>>>
>>> (again, I hope this works out visually. I have done the figure in
>>> fixed-width text).
>>>
>>> OpenJump's QA tool shows that there is an error in the enclosing polygon
>>> at the "bow-tie point", and that the enclosing polygon is a bad feature.
>>>
>>> The triangle polygons themselves are not shown as bad features. There
>>> are points shown at all corners of the triangles, ie there is no real
>>> "bow-tie" type self intersection.
>>>
>>> The enclosing polygon contains all the edges shown in the above figure,
>>> including those of the triangles. Each triangle is a separate polygon.
>>>
>>> I've traced the order of the edges of the enclosing polygon and it
>>> appears that it is the ordering of these edges that is creating the
>>> crossing / bow-tie in the enclosing polygon. That is, the enclosing
>>> polygon's points define the edges as follows:
>>>
>>> pt 0: se corner of east triangle
>>> pt 1: bow-tie point
>>> pt 2: nw corner of west triangle
>>> pt 3: sw corner of west triangle
>>> pt 4: bow-tie point
>>> pt 5: ne corner of east triangle
>>> ... and off to the remainder of the enclosing polygon points
>>>
>>> So it appears to me that the edges of the western triangle are actually
>>> traversed in the wrong order in the enclosing polygon. As well, clearly
>>> there is a self-intersection in the enclosing polygon.
>>>
>>> I conclude from this that the order of traversal of the western triangle
>>> edges could be reversed and preserve the clockwise traversal of the
>>> enclosing polygon's edges. However I think the fact that the bow-tie
>>> point is traversed twice in the same polygon is a real problem that must
>>> be repaired (manually in this case, I guess).
>>>
>>> Does anyone have any comments on this? Thanks in advance!
>>>
>>> Nicolas Ribot wrote:
>>>
>>>
>>>>> Good people;
>>>>>
>>>>> I have this odd problem that I hope others may clarify for me.
>>>>>
>>>>> I have a big ArcInfo polygon coverage produced by a sequence of
>>>>> spatial
>>>>> unions. One of the component polygon coverages was brutalized
>>>>> somewhere
>>>>> along the way and it has some polygons with triangular and bow-tie
>>>>> inclusions.
>>>>>
>>>>> Nevertheless, the coverage is clean and sober as far as ArcInfo is
>>>>> concerned.
>>>>>
>>>>> If you all can picture in your minds a bow-tie polygon |><| where the
>>>>> rightmost | of the bowtie is actually the edge of an enclosing
>>>>> polygon, kind
>>>>> of like:
>>>>>
>>>>> |
>>>>> |><|
>>>>> |
>>>>>
>>>>> (I sure hope that works out visually...)
>>>>>
>>>>> OK, when I use ogr2ogr to import this coverage into postgis 1.3.1 /
>>>>> geos-3.0.0rc4, I see the following:
>>>>>
>>>>>
>>>>>
>>>>> the containing polygon fails at st_isValid()
>>>>> the st_area() of the containing polygon appears to include the area
>>>>> of the
>>>>> bow-tie polygon, ie it is larger than the area copied over from the
>>>>> ArcInfo
>>>>> coverage by about the same amount as the area of the bow-tie
>>>>> polygon When I
>>>>> look at this little mess with OpenJump, sure enough the QA routines
>>>>> find the
>>>>> bow-tie and complain.
>>>>>
>>>>> The long and the short of this is that PostGIS returns slightly
>>>>> more area
>>>>> than ArcInfo does for the same big ugly polygon coverage, because
>>>>> of the
>>>>> apparent loss of these bow ties.
>>>>>
>>>>> What I'm not sure about is what exactly is wrong here. Is the
>>>>> bow-tie
>>>>> shape itself illegal? Or is it the fact that both sides of the
>>>>> bow-tie
>>>>> belong to the same polygon? Or something else I'm missing?
>>>>>
>>>>> Thanks for any light anyone can shed on this.
>>>>>
>>>>>
>>>>>
>>>>>
>>>> Hi,
>>>> I will only give a partial answer:
>>>> yes, a bowtie polygon is invalid for PostGIS (as stated in the OGC
>>>> SFSQL documentation, polygon's boundary cannot cross itself).
>>>> If you want to represent this with valid polygons, you will need 2
>>>> triangles touching at one point.
>>>>
>>>> HTH
>>>> nicolas
>>>> _______________________________________________
>>>> postgis-users mailing list
>>>> postgis-users at postgis.refractions.net
>>>> http://postgis.refractions.net/mailman/listinfo/postgis-users
>>>>
>>>>
>>>
>>>
>
>
>
--
Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022
More information about the postgis-users
mailing list